As the author of three dark and violent crime novels, Stieg Larsson was at home in a dysfunctional landscape of simmering resentments and rancourous family secrets. But the Swedish writer cannot have foreseen how, almost five years to the day after his death, the novels' success would lead to bitterness and paranoia in his own family.

In one of the most spectacular and unlikely ascents in recent literary history, Larsson, largely unknown before his sudden death at 50, has become one of the most successful writers in the world. Some 20 million of his books, the first of which was published in Britain as The Girl with the Dragon Tattoo, have been sold to date in Europe alone. Last year he was the world's second best selling author after Khaled Hosseini, author of The Kite Runner, and his estate is thought to be worth more than £20m.

But because he and the architect Eva Gabrielsson, his partner of 32 years, never married and he died without making a will, the proceeds have defaulted to his blood relations, provoking controversy in Sweden and displeasure from Gabrielsson.

Today in the latest episode in the acrimonious saga, Erland and Joakim Larsson, the author's father and brother, made Gabrielsson a public offer of £1.75mto settle the dispute, telling the Swedish paper Svenska Dagbladet, "We have to move on." Gabrielsson's response was curt: "You don't solve these things via media. It is so low. My lawyer will have to answer any further questions."

She has previously accused the Larsson family of seeking to "make money from someone who can't defend himself", saying it would make her partner "absolutely furious", and accusing Erland and Joakim of not being part of Stieg's life while he was alive.

But Erland Larsson said it was he who had insisted that his son write "something commercial", and that the Millennium trilogy, the third title of which was published in Britain last month as The Girl who Kicked the Hornet's Nest, was the result. Gabrielsson, he said, had resisted moves to come to a settlement.

"It's been almost five years since Stieg died. We have waited to come in contact with Eva but we can't wait another five years. Now we have to move on."

The acrimony over Larsson's estate surfaced a few months after his death from a heart attack in November 2004 while working as a dogged but comparatively obscure journalist, editing a Trotskyist periodical and an anti-fascist magazine, Expo, which he had founded. He had, it emerged, left the completed manuscripts for a series of three crime novels, the first of which was published the following year.

The surprise success of the novel has led, almost inevitably, to feverish interest from US directors and stars, with rumours that George Clooney, Johnny Depp, Quentin Tarantino and Martin Scorsese are among those interested in bringing a Hollywood version of the character of investigative journalist Mikael Blomkvist to the screen.

Gabrielsson says she and Larsson never married because he had believed his anti-fascist work could have put her at risk if there was a paper trail linking them legally or financially, but that he would have been dismayed to see anyone other than her in control of the estate. "It would have been beyond Stieg's worst nightmares to know that someone other than me was handling the rights to his books and to know that the money we planned to invest is gone," she has said. Others have agreed, setting up online campaigns in Scandinavia and beyond to raise money for Gabrielsson's legal fees.

Expo says that Larsson had wanted the proceeds of the Millennium trilogy to go to anti-fascist and domestic violence charities. A will dating from 1977, which was unwitnessed and therefore non-binding, expressed a wish for his assets to be left to a local branch of the Communist Workers League.

Erland and Joakim said yesterday their lives were unchanged despite their newfound wealth, telling the magazine: "We drive the same cars and live in the same houses as before." As a goodwill gesture, they were prepared to share something with Gabrielsson. "She was part of Stieg's life. She should have a safe and good life with this," said Joakim.

"No demands or anything. But she has to call and say yes please."

Gabrielsson's lawyer, Sara Pers-Krause, said that while she had been in contact with the Larssons' lawyer, no firm offer had been made. "They have to come with something concrete and we haven't had that yet. To just meet without any preconditions we have already done," she said.

"It was untrue that Gabrielsson had not been in contact with the family, accusing them of ignoring her," Pers-Krause said. "We want to make clear that the primary question for us is how to preserve his literary assets, and we have given them different suggestions for this since spring 2006 without receiving any reply."

Most intriguing remains Larsson's laptop computer, which according to Gabrielsson contains a 200-page manuscript for a sequel to the trilogy. In 2005 she refused an offer by the family to hand over the computer in exchange for the author's half of the flat they shared, which his father and brother had inherited. There is speculation that sketched outlines for six further novels are also contained in the laptop.